Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2304.03569 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of a solitonic vortex in an anisotropically trapped superfluid

Jose M. Gomez Llorente, Jesús Plata

Published Mar 10, 2023• 0 citations
arXivHTMLPDF

Abstract

Abstract We analytically study the dynamics of a solitonic vortex (SV) in a superfluid confined in a non-axisymmetric harmonic trap. The study provides a framework for analyzing the role of the trap anisotropy in the oscillation of SVs observed in recent experiments on atomic Bose and Fermi superfluids. The emergence of common and statistics-dependent features is traced in a unified approach to both types of fluid. Our description, built in the hydrodynamic formalism, is based on a Lagragian approach which incorporates the vortex location as dynamical parameters of a variational ansatz. Previous operative Hamiltonian pictures are recovered through a canonically traced procedure. Our results improve the understanding of the experimental findings. Some of the observed features are shown to be specific to the tri-axial anisotropy of the trap. In particular, we characterize the nontrivial dependence of the oscillation frequency on the trapping transversal to the vortical line. The study reveals also the crucial role played by the nonlinear character of the dynamics in the observed oscillation: for the considered experimental conditions, the frequency, and, in turn, the effective inertial mass of the vortex, are found to significantly depend on the amplitude of the generated motion. It is also uncovered how the coupling with collective modes of the fluid induces a non-negligible shift in the oscillation frequency. The appearance of fine-structure features in the SV trajectory is predicted.

DOI
10.1088/1361-6455/acc36e

Related papers

Dark-soliton dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential

Wen Wen, Changqing Zhao, Xiaodong Ma

We present an investigation of generation, dynamics, and stability of dark solitons in anisotropic Fermi gases for a range of particle numbers and trap aspect ratios within the framework of the order-parameter equation. We calculate the periods of dark solitons oscillating in a trap and find good agreement with the results based on the Bogoliubov--de Gennes equations. By studying the stability of initially off-center dark solitons under various tight transverse confinements in the unitarity limit, we not only give the criterion of dynamical stability, but also find that the soliton and a hybrid of solitons and vortex rings can be characterized by different oscillation periods. The stability criterion is not fulfilled by the parameters of the recent experiment of Yefsah et al. [Nature (London) 499, 426 (2013)]. Therefore, instead of a very slow oscillation as observed experimentally, we find that the created dark soliton undergoes a transverse snake instability with a collapse into vortex rings, which propagate in solitonlike manner with a nearly 2 times larger period.

arXiv:1309.7408•Physical Review A•Dec 11, 2013•22 citations

Variational approach to the snake instability of a Bose-Einstein condensate soliton

U. Tanyeri, M. A. Gürkan, Ahmet Keleş +1 more

Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.

arXiv:2507.04926•Physical Review A•Dec 23, 2025•0 citations

Dynamics of a vortex in a trapped Bose-Einstein condensate

Anatoly A. Svidzinsky, Alexander L. Fetter

We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of a vortex line as a function of the local gradient of the trap potential, the line curvature, and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for two-dimensional (2D) and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shaped condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shaped condensate than in a disk-shaped one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.

arXiv:cond-mat/0007139•Physical Review A•Nov 15, 2000•129 citations

Superfluid excitations in rotating two-dimensional ring traps

Guilherme Tomishiyo, Lucas Madeira, M. A. Caracanhas

We studied a rotating Bose–Einstein condensate confined in ring trap configurations that can be produced starting with a bubble trap confinement, approximated by a Mexican hat and shift harmonic oscillator potentials. Using a variational technique and perturbation theory, we determined the vortex configurations in this system by varying the interparticle interaction and the angular velocity of the atomic cloud. We found that the phase diagram of the system has macrovortex structures for small positive values of the interaction parameter, and the charge of the central vortex increases with rotation. Strengthening the atomic interaction makes the macrovortex unstable, and it decays into multiple singly charged vortices that arrange themselves in a lattice configuration. We also look for experimentally realizable methods to determine the vortex configuration without relying upon absorption imaging since the structures are not always visible in the latter. More specifically, we study how the vortex distribution affects the collective modes of the condensate by solving the Gross–Pitaevskii equation numerically and by analytical predictions using the sum-rule approach for the frequencies of the modes. These results reveal important signatures to characterize the macrovortices and vortex lattice transitions in the experiments.

arXiv:2212.11027•Physics of Fluids•Jun 1, 2024•5 citations

Dynamics of a Trapped Condensate

Лев П. Питаевский, S. Stringari

Abstract This chapter provides a general discussion of the dynamic behaviour characterizing a harmonically trapped interacting Bose gas. Explicit results for the frequencies of the collective oscillations were derived by using the hydrodynamic theory of superfluids. Both surface and oscillation of compressional nature are considered and a direct comparison is presented with available experimental results. Sum rules are used to characterize the behaviour of the oscillations. Finite-size as well as beyond-mean-field effects are considered. A special discussion is devoted to the study of large-amplitude oscillations and of the expansion of the gas. The anisotropic expansion predicted by hydrodynamic theory is discussed in a systematic way. An important part of the chapter concerns the study of the dynamic structure factor and its determination in experiments based on two-photon Bragg spectroscopy. Finally, the competition between single-particle and collective modes in the excitation spectrum of a harmonically trapped BEC is discussed.

•Jan 1, 2016•2 citations

Single vortex states in a confined Bose-Einstein condensate

Stavros Komineas, Nigel R. Cooper, N. Papanicolaou

It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.

arXiv:cond-mat/0508562•Physical Review A•Nov 21, 2005•25 citations
Abstract We analytically study the dynamics of a solitonic vortex (SV) in a superfluid confined in a non-axisymmetric harmonic trap. The study provides a framework for analyzing the role of the trap anisotropy in the oscillation of SVs observed in recent experiments on atomic Bose and Fermi superfluids. The emergence of common and statistics-dependent features is traced in a unified approach to both types of fluid. Our description, built in the hydrodynamic formalism, is based on a Lagragian approach which incorporates the vortex location as dynamical parameters of a variational ansatz. Previous operative Hamiltonian pictures are recovered through a canonically traced procedure. Our results improve the understanding of the experimental findings. Some of the observed features are shown to be specific to the tri-axial anisotropy of the trap. In particular, we characterize the nontrivial dependence of the oscillation frequency on the trapping transversal to the vortical line. The study reveals also the crucial role played by the nonlinear character of the dynamics in the observed oscillation: for the considered experimental conditions, the frequency, and, in turn, the effective inertial mass of the vortex, are found to significantly depend on the amplitude of the generated motion. It is also uncovered how the coupling with collective modes of the fluid induces a non-negligible shift in the oscillation frequency. The appearance of fine-structure features in the SV trajectory is predicted.
We present an investigation of generation, dynamics, and stability of dark solitons in anisotropic Fermi gases for a range of particle numbers and trap aspect ratios within the framework of the order-parameter equation. We calculate the periods of dark solitons oscillating in a trap and find good agreement with the results based on the Bogoliubov--de Gennes equations. By studying the stability of initially off-center dark solitons under various tight transverse confinements in the unitarity limit, we not only give the criterion of dynamical stability, but also find that the soliton and a hybrid of solitons and vortex rings can be characterized by different oscillation periods. The stability criterion is not fulfilled by the parameters of the recent experiment of Yefsah et al. [Nature (London) 499, 426 (2013)]. Therefore, instead of a very slow oscillation as observed experimentally, we find that the created dark soliton undergoes a transverse snake instability with a collapse into vortex rings, which propagate in solitonlike manner with a nearly 2 times larger period.
Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.
We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of a vortex line as a function of the local gradient of the trap potential, the line curvature, and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for two-dimensional (2D) and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shaped condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shaped condensate than in a disk-shaped one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.
We studied a rotating Bose–Einstein condensate confined in ring trap configurations that can be produced starting with a bubble trap confinement, approximated by a Mexican hat and shift harmonic oscillator potentials. Using a variational technique and perturbation theory, we determined the vortex configurations in this system by varying the interparticle interaction and the angular velocity of the atomic cloud. We found that the phase diagram of the system has macrovortex structures for small positive values of the interaction parameter, and the charge of the central vortex increases with rotation. Strengthening the atomic interaction makes the macrovortex unstable, and it decays into multiple singly charged vortices that arrange themselves in a lattice configuration. We also look for experimentally realizable methods to determine the vortex configuration without relying upon absorption imaging since the structures are not always visible in the latter. More specifically, we study how the vortex distribution affects the collective modes of the condensate by solving the Gross–Pitaevskii equation numerically and by analytical predictions using the sum-rule approach for the frequencies of the modes. These results reveal important signatures to characterize the macrovortices and vortex lattice transitions in the experiments.
Abstract This chapter provides a general discussion of the dynamic behaviour characterizing a harmonically trapped interacting Bose gas. Explicit results for the frequencies of the collective oscillations were derived by using the hydrodynamic theory of superfluids. Both surface and oscillation of compressional nature are considered and a direct comparison is presented with available experimental results. Sum rules are used to characterize the behaviour of the oscillations. Finite-size as well as beyond-mean-field effects are considered. A special discussion is devoted to the study of large-amplitude oscillations and of the expansion of the gas. The anisotropic expansion predicted by hydrodynamic theory is discussed in a systematic way. An important part of the chapter concerns the study of the dynamic structure factor and its determination in experiments based on two-photon Bragg spectroscopy. Finally, the competition between single-particle and collective modes in the excitation spectrum of a harmonically trapped BEC is discussed.
It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.